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A Marquette University Law School poll said Milwaukee Mayor Tom Barrett (right), who lost to Gov. Scott Walker (left) in the governor's race in 2010, has a 47 percent to 46 percent lead on the governor among registered voters.

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Gov. Scott Walker and Milwaukee Mayor Tom Barrett, one of the Democratic candidates hoping to face him in the June 5 recall election, are in a virtual dead heat in the days leading up to Tuesday's recall primary, according to a poll released Wednesday.

The Marquette University Law School also showed Barrett leading his Democratic rivals in Tuesday's recall primary.

Barrett, who lost to Walker in the governor's race in November 2010 by about 123,000 votes, or 5 percentage points, has a 47 percent to 46 percent lead on the governor among registered voters, the poll said. But among likely voters, the situation flips, and Walker leads by 1 percentage point, or 48 percent to 47 percent.

Both results are well within the poll's margin of error.

The Marquette poll was released less than 48 hours after the candidates' deadlines to file campaign finance reports, which showed Walker with an eye-popping cash advantage.

But the Marquette poll indicates the millions spent by Walker haven't led to him pulling ahead in the polls. These recent results are even closer than Marquette's March poll, when Walker led Barrett by 2 percentage points.

"Despite being vastly outspent and targeted by millions and millions of dollars from Scott Walker and his right-wing special interest allies, Tom Barrett is in a dead heat with Walker in the race for governor," said Barrett campaign spokesman Phil Walzak.

Walker did better against the other Democratic challengers, according to the poll. He led former Dane County Executive Kathleen Falk, the first Democrat into the recall race, by 49 percent to 42 percent among registered voters and 49 percent to 43 among likely voters.

"It's not surprising. The establishment has predicted this whole thing incorrectly. Who will decide this election are the people who have been going door to door," Falk said, speaking to reporters at a worker-owned taxi cooperative, Union Cab of Madison. "The people will decide. We will see on Election Day."

Walker also led state Sen. Kathleen Vinehout, D-Alma, and Secretary of State Doug La Follette by a wider margin of 49 percent to 40 percent.

The Democratic primary race has widened, according to the poll, with Barrett now leading Falk 38 percent to 21 percent, La Follette getting 8 percent and Vinehout getting 6 percent. The March Marquette poll had showed Barrett with 36 percent compared to Falk's 29 percent and La Follette and Vinehout at 8 percent each.

The pollsters also reportedly asked undecided voters who they were leaning toward. Including those leaning voters, the primary results become Barrett at 45 percent, Falk at 23 percent, La Follette at 8 percent and Vinehout at 8 percent, with another 9 percent saying they were undecided, the poll said.

"Despite Barrett's late entry into the race, he has improved his position both among Democratic primary voters and in the general recall contest against Walker," said political science professor Charles Franklin, who is a visiting professor at Marquette and director of the law school poll. "The contest is now essentially a tie."

The poll interviewed 705 registered Wisconsin voters by both land line and cellphone and was conducted April 26-29. It has a margin of error of plus or minus about four percentage points.

Walker spokesman Ciara Matthews said his campaign is confident heading into the June 5 recall, saying he had run in 2010 promising to close Wisconsin's budget deficit without widespread tax increases, layoffs of public employees, or making cuts to essential services.

"Gov. Walker has kept those promises, and we are confident that because the positive effects of his reforms continue to create more jobs and keep more money in the pockets of taxpayers, voters will reaffirm the decision they made a year ago," Matthews said.

— State Journal reporter Clay Barbour contributed to this report.